Nonstabilizerness in the unitary and monitored quantum dynamics of XXZ-staggered and SYK models

Abstract

We consider the quantum-state-diffusion dynamics of the XXZ-staggered spin chain, also focusing on its noninteracting XX-staggered limit, and of the Sachdev-Ye-Kitaev (SYK) model. We describe the process through quantum trajectories and evaluate the nonstabilizerness (also known as ``magic'') along the trajectories, quantified through the stabilizer Rényi entropy (SRE). In the absence of measurements, we find that the SYK model is the only one in which the time-averaged SRE saturates the random state bound and has a scaling with the system size that is well described by the theoretical prediction for quantum chaotic systems. In the presence of measurements, we numerically find that the steady-state SRE versus the coupling strength to the environment is well fitted by a generalized Lorentzian function. The scaling of the fitting parameters with the system size suggests that the steady-state} SRE linearly increases with the system size in all the considered cases, and displays no measurement-induced quantum transition, as confirmed by the curves of the steady-state SRE versus the system size.

12 pages, 6 figures, version accepted in PRB

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• Stabilizer Rényi Entropy and Conformal Field Theory
• Nonstabilizerness in open XXZ spin chains: Universal scaling and dynamics
• Stabilizer Rényi Entropy Encodes Fusion Rules of Topological Defects and Boundaries
• Operational interpretation of the Stabilizer Entropy
• Rise and fall of nonstabilizerness via random measurements
• Entanglement behavior and localization properties in monitored fermion systems
• Spectral signatures of nonstabilizerness and criticality in infinite matrix product states
• Connecting Magic Dynamics in Thermofield Double States to Spectral Form Factors
• Operator delocalization in disordered spin chains via exact MPO marginals